Does the Dot over a Lowercase "i" Have a Name?

That dot above the lower-case letters "i" and "j" is actually a diacritical mark called a tittle. The term "tittle" dates back to at least the 1500s and is often used in conjunction with the word "jot" in the phrase "every jot and tittle". The word "jot" is a transliteration of the Greek word "iota," the smallest letter of the Greek alphabet, hence the phrase "every jot and tittle" meaning every little thing or down to the last detail. Incidentally, a tittle is also the name for a dot on dice.

More facts about diacritical marks:

A diacritical mark is any kind of mark added to a letter to change its emphasis or pronunciation. Common diacritical marks include the acute, or right-slanted accent mark; the cedilla, which is a swirly line under a "c" in some French words; and the umlaut, or the double dots that can appear over vowels.

There are more than 10 kinds of diacritical marks in Anglicized alphabets alone, and even more in Arabic, Greek, or Asian character alphabets.

In English, diacritical marks usually indicate merely pronunciation or emphasis. In some languages, a diacritical mark can change the meaning or context of the word altogether. This is the case with the damma in Arabic or cantillation marks in Hebrew chants.